Daily Practice · Higher Plus
March 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1955 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1955y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 2nd March 1955A cuboid measures 9 cm by 6 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd March 1955A bag holds 3 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th March 1955On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th March 1955A car covers 450 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th March 1955f(x) = 2x + 9. Work out the inverse function f^-1(x).
- 7th March 1955y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 8th March 1955The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 9th March 1955A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 10th March 1955A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 11th March 1955Rationalise the denominator of 63/sqrt(7), giving your answer in its simplest form.
- 12th March 1955Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 13th March 1955y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 25.
- 14th March 1955In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 15th March 1955The probability of winning a game is 1/5. A player expects 20 wins. How many games did they play?
- 16th March 1955On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th March 1955Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 18th March 1955Use the iteration x(n+1) = cube root of (12x(n) + 8) with x(0) = 1. Work out x(1) to 3 decimal places.
- 19th March 1955A train slows steadily from 21 m/s to rest in 8 seconds. Work out its deceleration.
- 20th March 1955In a vector proof you find that vector PQ = 6a - 6b and vector RS = 30a - 30b. What does this show about PQ and RS?
- 21st March 1955A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 22nd March 1955A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 23rd March 1955A rectangle is 10 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th March 1955Work out the nth term of the quadratic sequence 13, 24, 39, 58, ...
- 25th March 1955y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 26th March 1955A cuboid measures 4 cm by 6 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th March 1955A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th March 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th March 1955Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 30th March 1955The point (-2, 2) lies on y = f(x). Write down its image on y = f(-x).
- 31st March 1955y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.